In addition to the organizations described in the Mongoose Traveller core books - the Army, Navy, Scouts, etc. - there are a number of organizations unique to the Boom Worlds setting.*
The Third Section
The Third Section is a subcommittee within the College of Thought. It's original purpose is long lost to history, but after the last war with the [Click] broke apart the last pieces of their empire, the Third Section became the Steering Committee's secret police. Due to issues of logistics and manpower, the Third Section is rarely deployed and, despite assertions to the contrary, the Directorate is not able to maintain anything close to a police state; however, when revenue begins to dry or Steering Committee members see their megacorps begin to hemorrhage profits, Third Section agents may be deployed. The results of these deployments are always disastrous.
The Bureau of Astropsychics
The ostensible purpose of the Bureau of Astropsychics is to train psychic-potentials in the art of psychic-astrogation. This art has led to the discovery and exploitation of a number of new sectors, as well as the creation of the mutants that make the extreme jumps required to access the Boom Worlds possible. However, it is a well known secret that the Bureau of Astropsychics also illegally trains a number of its members in the art of psychic warfare. These adepts are often hired out to Directorate authorities or feuding noble houses, making it unlikely that the members of the bureau will ever be prosecuted.
The Athena Group
One of the many megacorps of Directorate space, the Athena Group specializes in terraforming. Its greatest success is often said to be the planet Minerva, which currently acts as its corporate headquarters in the Boom Worlds. Athena is equally known for its infamous failure, the colony on Prometheus. The reasons for the colony's failure are a mystery to all but the highest level officials within the company. Many conspiracy theorists - at least those with any sense of the interstellar economy - assert that the Athena Group also serves as a weapons developer for the Third Section, or any number of other shadowy organizations.
The Pirates of Guthrum
Guthrum was one of the first planets settled after the Boom Worlds was discovered. Unfortunately for that first wave of settlers, the residual energies of the solar event had not yet calmed enough to prevent them from mutating. Now Guthrum is under Directorate interdiction, for its mutant population - which seems to be reasonably self-sustaining - often attacks those who enter their system. In addition to this, they are also known to engage in piracy and lead raids on nearby systems. Their brutality is legendary, but savvy free traders know that it is possible to reason with them.
The Oniax Syndicate
The solar event which created the Boom Worlds and destroyed the alien interstellar empire that once existed in that remote corner of space left in its wake the mutated descendants of a once glorious people. Some of these descendents have accepted Directorate rule, but few did so willingly. Directorate officials believe that the Oniax Syndicate is one of a number of "criminal" syndicates within the territory newly acquired by the Directorate based around pre-existing alien noble houses. The Oniax Syndicate is known to engage in piracy - sometimes alongside the Pirates of Guthrum, sometimes opposing them - and to be a large producer of the alien drug known simply as "juice," which seems to sooth the pain of the mutants produced in this region of space while having now affect on those with more standard biologies.
The Order of the Universal Principle
The Order of the Universal Principle is a strange movement that has taken the idea of a unified theory of physics to what Directorate officials consider an unhealthy extreme. They have eschewed scientific searches, preferring meditative rituals designed to align one's consciousness with that of the universe. These meditations often, bizarrely, occasionally lead them to commit assassinations, suicide bombings, and other acts of terror. These often coincide with the members of the Order ranting insanely about the secret significance of a "divine number." The precise digit has, so far, been different at each event. The Directorate considers them a great threat to the safety of its citizens.
Founded on Pinkerton, a metroworld close to Sublime Terra, Darkstar Defense initially served as a mercenaries during the [Click] Wars under the name Pythagoras Ltd. After several name changes, Darkstar Defense changed its roll to that of a privatized police force utilized on a number of metroworlds, particularly those owned by members of the Steering Committee or one of the Terran noble houses. They provide most of the security forces in the Boom Worlds, acting as customs agents, criminal investigators, and of course good old hired muscle.
A technical term for a supposed unified resistance group among the farmers and workers of the Boom Worlds, the existence of the OpProl is hotly debated outside the Steering Committee and its various colleges. Directorate propaganda attributes a large number of radical political views to this organization, including mandatory sterilization of all citizens who currently posses a faufreluches social standing of 8 or higher, affirmative action for Froguloids, Dogoids, reparations for the [Click], and some vague terror called "soshialsm." Whether or not these views are held by anyone the Directorate would identify as an OpProl, it is true that a number of farmers and workers have begun stockpiling weapons on the worlds of Ceres and Nibelung.
*In addition, I have renamed the TAS to the Traveller's Guild because guilds in my sci fi make me happy.